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[
{
"content": "Use python for all calculations. Give your answer inside \\boxed{}.",
"role": "system",
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"tool_calls": null
},
{
"content": "What is the degree of the polynomial $(4 +5x^3 +100 +2\\pi x^4 + \\sqrt{10}x^4 +9)$?",
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}
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[
{
"content": null,
"role": "assistant",
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{
"function": {
"arguments": "{\"code\":\"import math\\ncoeff_x4 = 2*math.pi + math.sqrt(10)\\ncoeff_x3 = 5\\nconst = 4+100+9\\ncoeff_x4, coeff_x3, const\\n\"}",
"name": "python",
"type": null
},
"id": "call_ED4thq0YnLxIVmhs9XyEJXYL",
"type": "function"
}
]
},
{
"content": "Out[1]: (9.445462967347966, 5, 113)",
"role": "tool",
"reasoning_content": null,
"tool_calls": null
},
{
"content": "\\boxed{4}",
"role": "assistant",
"reasoning_content": null,
"tool_calls": null
}
] |
[{"function": {"description": "Execute `code` inside persistent Python REPL.", "name": "python", "parameters": {"$defs": {"PythonWorkerState": {"additionalProperties": false, "properties": {"execution_count": {"title": "Execution Count", "type": "integer"}, "ready": {"title": "Ready", "type": "boolean"}}, "required": ["ready", "execution_count"], "title": "PythonWorkerState", "type": "object"}}, "additionalProperties": false, "properties": {"code": {"title": "Code", "type": "string"}}, "required": ["code"], "title": "python_args", "type": "object"}}, "type": "function"}]
|
[
{
"content": "Use python for all calculations. Give your answer inside \\boxed{}.",
"role": "system",
"reasoning_content": null,
"tool_calls": null
},
{
"content": "Evaluate $\\left\\lceil3\\left(6-\\frac12\\right)\\right\\rceil$.",
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"reasoning_content": null,
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}
] |
[
{
"content": null,
"role": "assistant",
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"function": {
"arguments": "{\"code\":\"import math\\nval = 3*(6-0.5)\\nres = math.ceil(val)\\nval, res\"}",
"name": "python",
"type": null
},
"id": "call_q0IaxpDIPFGvzpYg9pS8Sps2",
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}
]
},
{
"content": "Out[1]: (16.5, 17)",
"role": "tool",
"reasoning_content": null,
"tool_calls": null
},
{
"content": "\\boxed{17}",
"role": "assistant",
"reasoning_content": null,
"tool_calls": null
}
] |
[{"function": {"description": "Execute `code` inside persistent Python REPL.", "name": "python", "parameters": {"$defs": {"PythonWorkerState": {"additionalProperties": false, "properties": {"execution_count": {"title": "Execution Count", "type": "integer"}, "ready": {"title": "Ready", "type": "boolean"}}, "required": ["ready", "execution_count"], "title": "PythonWorkerState", "type": "object"}}, "additionalProperties": false, "properties": {"code": {"title": "Code", "type": "string"}}, "required": ["code"], "title": "python_args", "type": "object"}}, "type": "function"}]
|
[
{
"content": "Use python for all calculations. Give your answer inside \\boxed{}.",
"role": "system",
"reasoning_content": null,
"tool_calls": null
},
{
"content": "Let \\[f(x) = \\left\\{\n\\begin{array}{cl} ax+3, &\\text{ if }x>2, \\\\\nx-5 &\\text{ if } -2 \\le x \\le 2, \\\\\n2x-b &\\text{ if } x <-2.\n\\end{array}\n\\right.\\]Find $a+b$ if the piecewise function is continuous (which means that its graph can be drawn without lifting your pencil from the paper).",
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"reasoning_content": null,
"tool_calls": null
}
] |
[
{
"content": null,
"role": "assistant",
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{
"function": {
"arguments": "{\"code\":\"a = -3\\nb = 3\\nprint(a + b)\\n\"}",
"name": "python",
"type": null
},
"id": "call_kBznzmBhc5k9H4Qt3FWXuesQ",
"type": "function"
}
]
},
{
"content": "0",
"role": "tool",
"reasoning_content": null,
"tool_calls": null
},
{
"content": "\\boxed{0}",
"role": "assistant",
"reasoning_content": null,
"tool_calls": null
}
] |
[{"function": {"description": "Execute `code` inside persistent Python REPL.", "name": "python", "parameters": {"$defs": {"PythonWorkerState": {"additionalProperties": false, "properties": {"execution_count": {"title": "Execution Count", "type": "integer"}, "ready": {"title": "Ready", "type": "boolean"}}, "required": ["ready", "execution_count"], "title": "PythonWorkerState", "type": "object"}}, "additionalProperties": false, "properties": {"code": {"title": "Code", "type": "string"}}, "required": ["code"], "title": "python_args", "type": "object"}}, "type": "function"}]
|
[
{
"content": "Use python for all calculations. Give your answer inside \\boxed{}.",
"role": "system",
"reasoning_content": null,
"tool_calls": null
},
{
"content": "Sam is hired for a 20-day period. On days that he works, he earns $\\$$60. For each day that he does not work, $\\$$30 is subtracted from his earnings. At the end of the 20-day period, he received $\\$$660. How many days did he not work?",
"role": "user",
"reasoning_content": null,
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}
] |
[
{
"content": null,
"role": "assistant",
"reasoning_content": null,
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{
"function": {
"arguments": "{\"code\":\"n = 6\\nw = 20 - n\\nE = 60*w - 30*n\\nE\\n\"}",
"name": "python",
"type": null
},
"id": "call_iMz9VbXLf6Q8apARcxSxfCNN",
"type": "function"
}
]
},
{
"content": "Out[1]: 660",
"role": "tool",
"reasoning_content": null,
"tool_calls": null
},
{
"content": "Let n be the number of days not worked. Then he worked 20 − n days. Earnings:\n60(20 − n) − 30n = 660\n1200 − 60n − 30n = 660\n1200 − 90n = 660\n90n = 540\nn = 6\n\n\\boxed{6}",
"role": "assistant",
"reasoning_content": null,
"tool_calls": null
}
] |
[{"function": {"description": "Execute `code` inside persistent Python REPL.", "name": "python", "parameters": {"$defs": {"PythonWorkerState": {"additionalProperties": false, "properties": {"execution_count": {"title": "Execution Count", "type": "integer"}, "ready": {"title": "Ready", "type": "boolean"}}, "required": ["ready", "execution_count"], "title": "PythonWorkerState", "type": "object"}}, "additionalProperties": false, "properties": {"code": {"title": "Code", "type": "string"}}, "required": ["code"], "title": "python_args", "type": "object"}}, "type": "function"}]
|
[
{
"content": "Use python for all calculations. Give your answer inside \\boxed{}.",
"role": "system",
"reasoning_content": null,
"tool_calls": null
},
{
"content": "A rectangular band formation is a formation with $m$ band members in each of $r$ rows, where $m$ and $r$ are integers. A particular band has less than 100 band members. The director arranges them in a rectangular formation and finds that he has two members left over. If he increases the number of members in each row by 1 and reduces the number of rows by 2, there are exactly enough places in the new formation for each band member. What is the largest number of members the band could have?",
"role": "user",
"reasoning_content": null,
"tool_calls": null
}
] |
[
{
"content": null,
"role": "assistant",
"reasoning_content": null,
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{
"function": {
"arguments": "{\"code\":\"solutions = []\\nfor m in range(1,50):\\n r = 2*m+4\\n N = m*r + 2\\n if N == (m+1)*(r-2) and N < 100 and r>2:\\n solutions.append((N,m,r))\\nsolutions\\n\"}",
"name": "python",
"type": null
},
"id": "call_uqxEBotaIr6mKR7Ylwuy6zJw",
"type": "function"
}
]
},
{
"content": "Out[1]: [(8, 1, 6), (18, 2, 8), (32, 3, 10), (50, 4, 12), (72, 5, 14), (98, 6, 16)]",
"role": "tool",
"reasoning_content": null,
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{
"content": "\\boxed{98}\n\nReason:\n- Let N be total members, arranged as m per row in r rows with 2 left over: N = m r + 2.\n- After increasing per row by 1 and reducing rows by 2: N = (m+1)(r-2).\n- Equate: m r + 2 = (m+1)(r-2) ⇒ m r + 2 = (m+1)r - 2m - 2 ⇒ r = 2m + 4.\n- Then N = m(2m+4) + 2 = 2m^2 + 4m + 2.\n- N < 100 ⇒ 2m^2 + 4m + 2 < 100 ⇒ m ≤ 6.\n- For m = 1..6, N = 8, 18, 32, 50, 72, 98. The largest is 98 (with m = 6, r = 16).",
"role": "assistant",
"reasoning_content": null,
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}
] |
[{"function": {"description": "Execute `code` inside persistent Python REPL.", "name": "python", "parameters": {"$defs": {"PythonWorkerState": {"additionalProperties": false, "properties": {"execution_count": {"title": "Execution Count", "type": "integer"}, "ready": {"title": "Ready", "type": "boolean"}}, "required": ["ready", "execution_count"], "title": "PythonWorkerState", "type": "object"}}, "additionalProperties": false, "properties": {"code": {"title": "Code", "type": "string"}}, "required": ["code"], "title": "python_args", "type": "object"}}, "type": "function"}]
|
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